Since the 1980s, Fourier analysis methods have become of ever greater interest in the study
of linear and nonlinear partial differential equations. In particular, techniques based on …

Formulated and intensively studied at the beginning of the nineteenth century, the classical
partial differential equations of mathematical physics represent the foundation of our …

When estimating solutions of dissipative partial differential equations in L p-related spaces,
we often need lower bounds for an integral involving the dissipative term. If the dissipative …

In previous works by the first two authors, classes of initial data to the three-dimensional,
incompressible Navier-Stokes equations were presented, generating a global smooth …

This text consists in notes on a series of lectures given in March 2004 in the De Giorgi center
during a semester about” Phase Space Analysis of Partial Differential Equations”. The goal …

In [J.-Y. Chemin, I. Gallagher, On the global wellposedness of the 3-D Navier–Stokes
equations with large initial data, Annales Scientifiques de l'École Normale Supérieure de …

We revisit the regularity theory of Escauriaza, Seregin, and\v {S} ver\'ak for solutions to the
three-dimensional Navier-Stokes equations which are uniformly bounded in the critical $ L …

In this paper, we investigate the large‐time decay and stability to any given global smooth
solutions of the 3‐D incompressible inhomogeneous Navier‐Stokes equations. In particular …

We study the 3D hyperdissipative Navier-Stokes equations on the torus, where the viscosity
exponent α can be larger than the Lions exponent 5/4. It is well-known that, due to Lions [1] …

We prove that if an initial datum to the incompressible Navier–Stokes equations in any
critical Besov space ̇ B^-1+\frac 3p _ p, q (R^ 3) B˙ p, q-1+ 3 p (R 3), with 3< p, q< ∞ 3< p …